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    "# Plots\n",
    "\n",
    "This file demonstrates how to create plots in Julia by using the [Plots](https://github.com/JuliaPlots/Plots.jl) package (using PyPlot or GR as the backend).\n",
    "\n",
    "See [Julia Plots Gallery](https://goropikari.github.io/PlotsGallery.jl/) for examples (with code snippets)."
   ]
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    "using Dates, Plots\n",
    "\n",
    "#pyplot(size=(500,333))\n",
    "gr(size=(480,320))\n",
    "default(fmt = :svg)"
   ]
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   "cell_type": "markdown",
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   "source": [
    "# A First Plot\n",
    "\n",
    "The next cell creates and shows a first plot.\n",
    "\n",
    "The first plot takes a bit of time. Subsequent plots are much quicker.\n",
    "\n",
    "The $x$ and $y$ values in this file are in vectors and matrices, so all the examples can be applied to (statistical) data. (In contrast, when your aim is to plot functions, then you can actually avoid generating the y values. See the manual for a discussion.)\n",
    "\n",
    "The `savefig()` command in the third cell saves the plot to a graphics file."
   ]
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    "x = range(-3,stop=3,length=20)      #something to plot\n",
    "y = 2*x.^2 .+ 0.5\n",
    "\n",
    "p1 = plot( [x x],[y log.(y)],\n",
    "           label = [\"y\" \"log y\"],\n",
    "           linecolor = [:red :blue],\n",
    "           linestyle = [:solid :dot],\n",
    "           linewidth = [5 2] )"
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      "linestyle {Symbol}\n",
      "linestyles, ls, s, style\n",
      "\n",
      "Style of the line (for path and bar stroke).  Choose from Symbol[:auto, :solid, :dash, :dot, :dashdot, :dashdotdot]\n",
      "Series attribute,  default: solid\n"
     ]
    }
   ],
   "source": [
    "plotattr(\"linestyle\")             #see all available options"
   ]
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       "</g>\n",
       "<g clip-path=\"url(#clip4400)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:84px; text-anchor:middle;\" transform=\"rotate(0, 1035.16, 598.197)\" x=\"1035.16\" y=\"598.197\">here</text>\n",
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      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#now with title, labels and more\n",
    "\n",
    "p1 = plot( [x x],[y log.(y)],\n",
    "           label = [\"y\" \"log y\"],\n",
    "           legend = :top,\n",
    "           linecolor = [:red :blue],\n",
    "           linestyle = [:solid :dot],\n",
    "           linewidth = [5 2],\n",
    "           title = \"a title\",\n",
    "           titlefont = font(20),\n",
    "           xlabel = \"x\",\n",
    "           ylabel = \"function values\",\n",
    "           xlims = (-3.5,3.5),\n",
    "           ylims = (-1,15),\n",
    "           xticks = [-2;0;2],\n",
    "           yticks = [0;5;6;10],\n",
    "           annotation = ([-1.9,0],[0.9,8],[text(\"some text\",8),\"here\"]) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "savefig(\"AFirstPlot.pdf\")              #change to .svg or .png"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Subplots\n",
    "\n",
    "Use ```layout=(2,2)``` to create a 2x2 plot. You can make some of the subplots blank."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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       "<text style=\"fill:#ffffff; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 1338.48, 1142.03)\" x=\"1338.48\" y=\"1142.03\">0.6</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip4900)\">\n",
       "<text style=\"fill:#ffffff; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 1338.48, 1040.6)\" x=\"1338.48\" y=\"1040.6\">0.8</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip4900)\">\n",
       "<text style=\"fill:#ffffff; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 1338.48, 939.175)\" x=\"1338.48\" y=\"939.175\">1.0</text>\n",
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       "</svg>\n"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1 = plot( [x x x],[y log.(y) log.(y).^2],\n",
    "           layout = (2,2),\n",
    "           size = (600,400),\n",
    "           linecolor = [:red :blue :black],\n",
    "           title = [\"a. first\" \"b. second\" \"c. third\"],\n",
    "           xlabel = \"x\",\n",
    "           legend = false )\n",
    "\n",
    "plot!(p1[2,2],legend=false,grid=false,foreground_color_subplot=:white)      #modify subplot [2,2] to be blank"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adding Horizontal and Vertical Lines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
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       "<g clip-path=\"url(#clip5300)\">\n",
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       "<g clip-path=\"url(#clip5300)\">\n",
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       "<g clip-path=\"url(#clip5300)\">\n",
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      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1 = plot( x,y,\n",
    "           legend = false,\n",
    "           title = \"With reference lines at y = 11 and x = 0.5\",\n",
    "           xlabel = \"x\",\n",
    "           ylabel = \"function values\" )\n",
    "\n",
    "vline!([0.5],linecolor=:red,line=(:dot,2))   #easiest to not integrate this in plot()\n",
    "hline!([11],linecolor=:black,line=(:dash,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# LaTeX in the Figure\n",
    "\n",
    "Notice: you probably need LaTeX installed on the computer for this run. Also, you may be asked to install some further LaTeX packages and fonts.\n",
    "\n",
    "Also, saving figures with LaTeX creates large pdf files if you use `gr()`. Consider either using `pyplot()` for this or save to png/svg (not pdf) instead."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
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       "</g>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using LaTeXStrings                 #add some LaTeX to the figure\n",
    "\n",
    "p1 = plot( x,y,legend = false,\n",
    "           title = L\"$\\mathrm{a \\ title \\ using \\ LaTeX,\\ } 2 b^2 + 0.5$\",\n",
    "           xlabel = L\"$\\alpha$\",\n",
    "           ylabel = \"function values\",\n",
    "           annotation = (-0.5,10,L\"$\\mu_2 = \\int x^2 f(x) dx$\") )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "savefig(\"ASecondPlot.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bars and Stairs Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
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     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "p1 = bar( x,y,\n",
    "          legend = false,\n",
    "          fillcolor = :red,\n",
    "          xlims = (-2.5,2.5),\n",
    "          ylims = (-1,15),\n",
    "          title = \"Bar chart\" )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
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     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "p1 = plot( x,y,\n",
    "           linetype = :steppre,\n",
    "           linecolor = :red,\n",
    "           legend = false,\n",
    "           xlims = (-2.5,2.5),\n",
    "           ylims = (-1,15),\n",
    "           title = \"Stairs plot\" )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Surface Plot\n",
    "\n",
    "In case the surface plot (below) does not work with the default backend (`gr()`), switch over to ```pyplot(size=(500,333))``` and then try again. (This seems to be an issue on some Julia versions/some operating systems.) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(20,)(25,)(25, 20)\n"
     ]
    },
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      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = range(-3,stop=3,length=20)       #create some \"data\" to plot\n",
    "y = range(1,stop=7,length=25)\n",
    "\n",
    "z = fill(NaN,(length(x),length(y)))  #to put results in, initialized as NaNs\n",
    "for j = 1:length(y)                  #create z2 column by column\n",
    "  z[:,j] = 2*x.^2 .+ (y[j]-4)^2 - 0.0*x.*(y[j]-4)\n",
    "end\n",
    "\n",
    "#notice the arguments: x,y,z'\n",
    "println(size(x),size(y),size(z'))\n",
    "\n",
    "#pyplot(size=(500,333))                   #in case surface does not work with gr()\n",
    "p1 = surface( x,y,z',\n",
    "              size = (600,433),\n",
    "              legend = false,\n",
    "              xlims = (-3,3),\n",
    "              ylims = (1,7),\n",
    "              zlims = (0,30),\n",
    "              title = \"Surface plot\" )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1 = surface( x,y,z',\n",
    "              size = (600,433),\n",
    "              camera = (60,30),\n",
    "              legend =false,\n",
    "              xlims = (-3,3),\n",
    "              ylims = (1,7),\n",
    "              zlims = (0,30),\n",
    "              title = \"Surface plot, rotated\" )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Contour Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
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      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1 = contour(x,y,z',                 #notice the transpose: z'\n",
    "            legend = false,\n",
    "            title = \"Contour plot of loss function\",\n",
    "            xlabel = \"x\",\n",
    "            ylabel = \"y\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Scatter and Histogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "markershape {Symbol, Shape, or AbstractVector}\n",
      "markershapes, shape\n",
      "\n",
      "Choose from Symbol[:none, :auto, :circle, :rect, :star5, :diamond, :hexagon, :cross, :xcross, :utriangle, :dtriangle, :rtriangle, :ltriangle, :pentagon, :heptagon, :octagon, :star4, :star6, :star7, :star8, :vline, :hline, :+, :x].\n",
      "Series attribute,  default: none\n"
     ]
    }
   ],
   "source": [
    "plotattr(\"markershape\")                #to see available options"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
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   "source": [
    "N = 51\n",
    "x = randn(N)\n",
    "y = rand(N)\n",
    "\n",
    "p1 = scatter( x,y,\n",
    "              markersize = 5,\n",
    "              markercolor = :grey,\n",
    "              markershape = :rect,\n",
    "              legend = false,\n",
    "              grid = false,\n",
    "              title = \"Scatter plot\",\n",
    "              xlabel = \"x\",\n",
    "              ylabel = \"y\" )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
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     "execution_count": 17,
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   ],
   "source": [
    "p1 = histogram( x,\n",
    "                bins = -2.5:0.25:2.5,\n",
    "                normalize = true,\n",
    "                fillcolor = :lightblue,\n",
    "                legend = false, \n",
    "                title = \"Histogram (with area = 1)\",\n",
    "                xlabel = \"x\",\n",
    "                ylabel = \"no. observations\" )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Time Series Plots\n",
    "\n",
    "We can use a `Date()` vector as the x-axis variable.\n",
    "\n",
    "To insert lines, annotations and tick marks, the $x$ values are defined as, for instance, `Dates.value(Date(2016,8,1))`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
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     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dN = Date(2015,12,4):Dates.Day(1):Date(2016,12,31)   #just faking some dates\n",
    "y  = randn(length(dN))                               #some random numbers to plot \n",
    "\n",
    "p1 = plot( dN,cumsum(y),\n",
    "           linecolor = :red,\n",
    "           legend = false,\n",
    "           title = \"A random walk\" )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
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       "<polyline clip-path=\"url(#clip9400)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
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       "<polyline clip-path=\"url(#clip9400)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
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       "<g clip-path=\"url(#clip9400)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 339.16, 1222.27)\" x=\"339.16\" y=\"1222.27\">2016</text>\n",
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       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 1828.84, 1222.27)\" x=\"1828.84\" y=\"1222.27\">2017</text>\n",
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       "<g clip-path=\"url(#clip9400)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 158.008, 847.309)\" x=\"158.008\" y=\"847.309\">2.5</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip9400)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 158.008, 698.122)\" x=\"158.008\" y=\"698.122\">5.0</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip9400)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 158.008, 548.934)\" x=\"158.008\" y=\"548.934\">7.5</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip9400)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 158.008, 399.747)\" x=\"158.008\" y=\"399.747\">10.0</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip9400)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 158.008, 250.559)\" x=\"158.008\" y=\"250.559\">12.5</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip9400)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:84px; text-anchor:middle;\" transform=\"rotate(0, 1024.98, 73.2)\" x=\"1024.98\" y=\"73.2\">A random walk, with better tick marks</text>\n",
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      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xTicksLoc = Dates.value.([Date(2016,1);Date(2016,7);Date(2017,1)])\n",
    "xTicksLab = [\"2016\";\"July\";\"2017\"]  #crude way of getting the tick marks right\n",
    "\n",
    "p1 = plot( dN,cumsum(y),\n",
    "           linecolor = :red,\n",
    "           legend = false,\n",
    "           xticks = (xTicksLoc,xTicksLab),\n",
    "           title = \"A random walk, with better tick marks\",\n",
    "           annotation = (Dates.value(Date(2016,5,1)),0.0,text(\"some text\",8)) )\n",
    "\n",
    "vline!([Dates.value(Date(2016))],linecolor=:black,line=(:dash,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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